Improve performance of x**y when y is a huge value (#438)

When y.exponent is several thousand or more, x**y was slow because exponentiation by squaring requires several thousands of multiplications.
Use exp and log in such case.
Needed to calaculate (1+1/n).power(n, prec)

Author: tompng

lib/bigdecimal.rb

@@ -165,22 +165,25 @@ def power(y, prec = nil)
       return BigDecimal(1).div(inv, prec)
     end
 
-    int_part = y.fix.to_i
     prec2 = prec + BigDecimal.double_fig
-    pow_prec = prec2 + (int_part > 0 ? y.exponent : 0)
-    ans = BigDecimal(1)
-    n = 1
-    xn = x
-    while true
-      ans = ans.mult(xn, pow_prec) if int_part.allbits?(n)
-      n <<= 1
-      break if n > int_part
-      xn = xn.mult(xn, pow_prec)
-    end
-    unless frac_part.zero?
-      ans = ans.mult(BigMath.exp(BigMath.log(x, prec2).mult(frac_part, prec2), prec2), prec2)
+
+    if frac_part.zero? && y.exponent < Math.log(prec) * 5 + 20
+      # Use exponentiation by squaring if y is an integer and not too large
+      pow_prec = prec2 + y.exponent
+      n = 1
+      xn = x
+      ans = BigDecimal(1)
+      int_part = y.fix.to_i
+      while true
+        ans = ans.mult(xn, pow_prec) if int_part.allbits?(n)
+        n <<= 1
+        break if n > int_part
+        xn = xn.mult(xn, pow_prec)
+      end
+      ans.mult(1, prec)
+    else
+      BigMath.exp(BigMath.log(x, prec2).mult(y, prec2), prec)
     end
-    ans.mult(1, prec)
   end
 
   # Returns the square root of the value.

test/bigdecimal/test_bigdecimal.rb

@@ -1991,6 +1991,11 @@ def test_power_with_rational
     assert_in_epsilon(z2, x2 ** y, 1e-99)
   end
 
+  def test_power_with_huge_value
+    n = BigDecimal('7e+10000')
+    assert_equal(BigMath.exp(1, 100), (1 + BigDecimal(1).div(n, 120)).power(n, 100))
+  end
+
   def test_power_precision
     x = BigDecimal("1.41421356237309504880168872420969807856967187537695")
     y = BigDecimal("3.14159265358979323846264338327950288419716939937511")